The present disclosure relates generally to extremum-seeking control strategies. The present disclosure relates more particularly to regulating, via extremum-seeking control, a variable of interest (e.g., power production, power consumption, rate of refrigerant flow, etc.) in an energy system.
Extremum-seeking control (ESC) is a class of self-optimizing control strategies that can dynamically search for the unknown and/or time-varying inputs of a system for optimizing a certain performance index. It can be considered a dynamic realization of gradient searching through the use of dither signals. The gradient of the system output with respect to the system input is typically obtained by slightly perturbing the system operation and applying a demodulation measure. Optimization of system performance can be obtained by driving the gradient towards zero by using an integrator in the closed-loop system. ESC is a non-model based control strategy, meaning that a model for the controlled system is not necessary for ESC to optimize the system. ESC has been used in many different engineering applications (e.g., combustion, circuitry, mining, aerospace and land-based vehicles, building HVAC, wind and solar energy, etc.) and has been shown to be able to improve the operational efficiency and performance for these engineering applications.
Although ESC does not require a model of the system to optimize the system output, properly configuring an ESC system may require knowledge of the system bandwidth (e.g., the natural frequency ωn of the plant) to select the frequency ωd of the dither signal. For example, it may be desirable to select a dither signal frequency ωd that is the same or similar to the natural frequency ωn of the plant to enhance the effect of the dither signal d on the performance variable y (e.g., by increasing the resonance between the dither signal d and the plant). Additionally, it may be desirable to know the system gain Ks in order to properly set the rate of gradient descent.
Traditional ESC systems require manual configuration and testing to determine suitable values for system parameters such as the system bandwidth and system gain. For example, a manual step test system identification procedure can be performed to estimate the system bandwidth. However, such testing requires disturbing the system (causing operation disruption) and assumes that the bandwidth does not change after testing. It would be desirable to provide an automatic configuration procedure that is non-disruptive and can automatically determine system parameters without requiring manual testing and configuration.